# 0.1 Optimizing logistic regression for a particle physics application

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This is an application module describing using Logistic Regression to solve a detection problem in Particle Physics: Detecting the top quark.

## Motivation

High-energy particle physics experiments today usually involves colliding beams of particles accelerated to tremendous energies and then studying the “shrapnel" that is created. The goal of such experiments often involves the discovery of new particles that are created when two common particles from the beams collide. Unfortunately, these new particles are so short-lived that they cannot be observed directly. Instead, the existence of such particles is inferred from patterns in the “shrapnel" that is formed when they decay into other particles. It is the properties of these secondary particles that are measured in detectors such as those at the Large Hadron Collider (LHC).

To discover a new particle, physicists use computer programs that have been programmed with theoretical models to simulate large numbers of random particle collisions. The models are tuned so as to generate two sets of collision “events": one set is compatible with the particle existing in nature and the other is compatible with the null hypothesis. The characteristics of the sets of simulated events are then compared with real events from a live experimental detector.

Because of the complicated nature of the events and the large amount of data involved, machine learning has been investigated to help with the classification problem of determining what kind of particles are initially produced for each event. If we can train classifiers on simulated data to be effective at distinguishing events that are associated with interesting particles from uninteresting background events, we will likely be able to use such classifiers to confirm or deny the discovery of these particles in real data. The existence of more effective classifiers decrease the amount of real data that must be collected to obtain a statistically significant result. Given the large expense of operating particle colliders and the power of modern computers, acquiring more effective classifiers is an important problem for particle physicists.

## Project goal

The project goal is to construct a classifier that is efficient at verifying the existence of a top quark in a set of simulated collision events. Top quarks are good particles for investigating classifiers because they are very rare and very hard to detect but have already been proven to exist. Efficiency is defined by the beam luminosity needed to detect the existence of top quarks with $5\sigma$ of statistical significance, the “industry standard" for particle physics. Beam luminosity is directly proportional to the number of collisions, and thus the operating time of the experiment, and thus the cost, so lower required luminosity is better.

Top quarks can be created by a number of different pathways, and each pathway creates a different pattern of decay products measured by the detectors, real or simulated. This project focuses on only one particular pathway which results in the creation of a top quark and its anti-particle in what are known as “t-tbar" events.

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